An encompassed representation of timescale hierarchies in first-order reaction network.

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

Unveiling the Nature of Chemical Bonds in Real Space.

Recent advent of diverse chemical entities necessitates a re-evaluation of chemical bond concepts, underscoring the importance of experimental evidence. Our prior study introduced a general methodology, termed Core Differential Fourier Synthesis (CDFS), for mapping the distribution of valence electron density (VED) in crystalline substances within real space. In this study, we directly compare the VED distributions obtained through CDFS with those derived from high-accuracy theoretical calculation using long-range corrected density functional theory, which quantitatively reproduces accurate orbital energies. This comparison serves to demonstrate the precision of the CDFS in replicating complex details. The VED patterns observed experimentally exhibited detailed structures and phases of wave functions indicative of sp3 hybrid orbitals, closely aligning with theoretical predictions. This alignment underscores the utility of our approach in gathering quantum chemical data experimentally, a crucial step for discussing the chemical properties, such as reaction mechanisms.

Ab initio molecular dynamics study of intersystem crossing dynamics for MH2 (M = Si, Ge, Sn, Pb) on spin-pure and spin-mixed potential energy surfaces.

Recently, surface-hopping ab initio molecular dynamics (SH-AIMD) simulations have come to be used to discuss the mechanisms and dynamics of excited-state chemical reactions, including internal conversion and intersystem crossing. In dynamics simulations involving intersystem crossing, there are two potential energy surfaces (PESs) governing the motion of nuclei: PES in a spin-pure state and PES in a spin-mixed state. The former gives wrong results for molecular systems with large spin-orbit coupling (SOC), while the latter requires a potential gradient that includes a change in SOC at each point, making the computational cost very high. In this study, we systematically investigate the extent to which the magnitude of SOC affects the results of the spin-pure state-based dynamics simulations for the hydride MH2 (M = Si, Ge, Sn, Pb) by performing SH-AIMD simulations based on spin-pure and spin-mixed states. It is clearly shown that spin-mixed state PESs are indispensable for the dynamics simulation of intersystem crossing in systems containing elements Sn and Pb from the fifth period onward. Furthermore, in addition to the widely used Tully's fewest switches (TFS) algorithm, the Zhu-Nakamura (ZN) global switching algorithm, which is computationally less expensive, is applied to SH for comparison. The results from TFS- and ZN-SH-AIMD methods are in qualitative agreement, suggesting that the less expensive ZN-SH-AIMD can be successfully utilized to investigate the dynamics of photochemical reactions based on quantum chemical calculations.

Guest-Responsive Near-Infrared-Luminescent Metal-Organic Cage Organized by Porphyrin Dyes and Yb(III) Complexes.

Metal-organic cages (MOCs) with luminophores have significant advantages for the facile detection of specific molecules based on turn-on or turn-off luminescence changes induced by host-guest complexation. One important challenge is the development of turn-on-type near-infrared (NIR)-luminescent MOCs. In this study, we synthesized a novel MOC consisting of two porphyrin dyes linked by four Yb(III) complexes, which exhibit bimodal red and NIR fluorescence signals upon photoexcitation of the porphyrin π system. Single-crystal X-ray structural analysis and computational molecular modeling revealed that planar aromatic perfluorocarbons were intercalated into the MOC. The tight packing between the MOC and guests enhanced the NIR fluorescence of Yb(III) by suppressing energy transfer from the photoexcited porphyrin to oxygen molecules. Guest-responsive turn-on NIR fluorescence changes in an MOC were successfully demonstrated.

Advanced theoretical design of light-driven molecular rotary motors: enhancing thermal helix inversion and visible-light activation.

In this study, we have advanced the field of light-driven molecular rotary motors (LDMRMs) by achieving two pivotal goals: lowering the thermal helix inversion (THI) barrier and extending the absorption wavelength into the visible spectrum. This study involves the structural reengineering of a second-generation visible LDMRM, resulting in the synthesis of a novel class, specifically, 2-((2S)-5-methoxy-2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-yl)-3-oxo-2,3-dihydro-1H-dibenzo[e,g]indole-6,9-dicarbonitrile. This redesigned motor stands out with its two photoisomerization stages and two thermal helix inversions, featuring exceptionally low THI barriers (4.00 and 2.05 kcal mol-1 at the OM2/MRCI level for the EM → EP and ZM → ZP processes, respectively). Moreover, it displays absorption wavelengths in the visible light range (482.98 and 465.76 nm for the EP and ZP isomers, respectively, at the TD-PBE0-D3/6-31G(d,p) level), surpassing its predecessors in efficiency, as indicated by the narrow HOMO-LUMO energy gap. Ultrafast photoisomerization kinetics (approximately 0.8-1.6 ps) and high quantum yields (around 0.3-0.6) were observed through trajectory surface hopping simulations. Additionally, the simulated time-resolved fluorescence emission spectrum indicates a significantly reduced "dark state" duration (0.09-0.26 ps) in these newly designed LDMRMs compared to the original ones, marking a substantial leap forward in the design and efficiency of LDMRMs.

Near-field induced local excitation dynamics of Na10 and Na10-N2 from real-time TDDFT.

Electron dynamics of the Na10 chain and the Na10-N2 complex locally excited by an atomistic optical near-field are investigated using real-time time-dependent density functional theory calculations on real-space grids. Ultrafast laser pulses were used to simulate the near-field excitation under on- and off-resonance conditions. Off-resonance excitation did not lead to the propagation of the excitation through the Na10 chain. In contrast, under the resonance conditions, the excited state is delocalized over the entire Na chain. Analysis of the local dipole moment of each atom in Na10 indicates that this behavior is consistent with the transition density. Adding an N2 molecule to the opposite end of the local excitation region results in energy transfer via the Na10 chain. The energy transfer efficiency of the N2 molecule is well correlated with the absorption spectrum of Na10. The present study paves the way for realizing remote excitation and photonic devices at the atomic scale.

Chiral Tetrakis Eu(III) Complexes with Ammonium Cations for Improved Circularly Polarized Luminescence.

Large dissymmetry factor of the circularly polarized luminescence (gCPL) was observed in ligand and coordination tuned chiral tetrakis europium (Eu(III)) complexes with ammonium cations. The gCPL value was estimated to be -1.54, which is the largest among chiral luminescent molecules. Through photophysical measurements, single crystal X-ray structural analyses and quantum chemical calculations, changes in the geometric and electronic structures were observed for a series of chiral tetrakis Eu(III) complexes which enhanced the gCPL value. The emission quantum yield and photosensitized energy transfer efficiencies of chiral Eu(III) complexes with ammonium cations were also larger than those of chiral Eu(III) complex with Cs+. Based on the systematic modifications and analyses for chiral tetrakis Eu(III) complex, effect of the ammonium cation on enhanced CPL brightness is reported.

A Steric-Repulsion-Driven Clutch Stack of Triaryltriazines: Correlated Molecular Rotations and a Thermoresponsive Gearshift in the Crystalline Solid.

We report that a newly developed type of triaryltriazine rotor, which bears bulky silyl moieties on the para position of its peripheral phenylene groups, forms a columnar stacked clutch structure in the crystalline phase. The phenylene units of the crystalline rotors display two different and interconvertible correlated molecular motions. It is possible to switch between these intermolecular geared rotational motions via a thermally induced crystal-to-crystal phase transition. Variable-temperature solid-state 2H NMR measurements and X-ray diffraction studies revealed that the crystalline rotor is characterized by a vertically stacked columnar structure upon introducing a bulky Si moiety with bent geometry as the stator. The structure exhibits correlated flapping motions via a combination of 85° and ca. 95° rotations between 295 and 348 K, concurrent with a negative entropy change (ΔS‡ = -23 ± 0.3 cal mol-1 K-1). Interestingly, heating the crystal beyond 348 K induces an anisotropic expansion of the column and lowers the steric congestion between the adjacent rotators, thus altering the correlated motions from a flapping motion to a correlated 2-fold 180° rotation with a lower entropic penalty (ΔS‡ = -14 ± 0.5 cal mol-1 K-1). The obtained results of our study suggest that the intermolecular stacking of the C3-symmetric rotator driven by the steric repulsion of the bulky stator represents a promising strategy for producing various correlated molecular motions in the crystalline phase. Moreover, direct and reversible modulation of the intermolecularly correlated rotation is achieved via a thermally induced crystal-to-crystal phase transition, which operates as a gearshift function at the molecular level.

Total and orbital density-based analyses of molecules revealing long-range interaction regions.

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO - 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

Reactive orbital energy theory serving a theoretical foundation for the electronic theory of organic chemistry.

It is established that the reactive orbital energy theory (ROET) theoretically reproduces the rule-based electronic theory diagrams of organic chemistry by a comparative study on the charge transfer natures of typical organic carbon-carbon and carbon-heteroatom bond formation reactions: aldol, Mannich, α-aminooxylation, and isogyric reactions. The ROET, which is an expansion of the reaction electronic theories (e.g., the frontier orbital theory) in terms of orbital energies, elucidates the reactive orbitals driving reactions and the charge transferability indices of the reactions. Performing the ROET analyses of these reactions shows that the charge transfer directions given in the rule-based diagrams of the electronic theory are reproduced even for the functional groups of charge transfer destinations in all but only two processes for 38 reaction processes. The ROET analyses also make clear the detailed orbital-based pictures of these bond formation reactions: that is, the use of the out-of-plane antibonding π orbitals in acidic conditions (enol-mode) and in-plane antibonding π orbitals in basic conditions (enolate-mode), which explain the experimentally assumed mechanisms such as the π-bond formations in acidic conditions and σ-bond formations at α-carbons in basic conditions. Furthermore, the ROET analyses explicate that the methyl group initially accepts electrons and then donates them to the bond formations in the target reactions. It is, consequently, suggested that the ROET serves a theoretical foundation for the electronic theory of organic chemistry.

Dimetal-Binding Scaffold 2-(Pyridin-2-yl)imidazo [1,5-b]pyridazine-7-ylidene: Synthesis of Trinuclear Heterobimetallic Complexes Involving Gold-Metal Interactions.

As a dimetal-binding rigid scaffold, 2-(pyridin-2-yl)imidazo[1,5-b]pyridazine-7-ylidene was introduced. The scaffold was first converted into a meridional Au,N,N-tridentate ligand through binding of a Au(I)Cl moiety at the carbene center. The Au(I) center and the N,N-chelating moiety were expected to function as metallophilic and 4e-σ-donative interaction sites, respectively, in the binding of the second metal center. In this manner, various trinuclear heterobimetallic complexes were synthesized with different 3d-metal sources, such as cationic CuI , CuII , NiII , and CoII salts. SC-XRD analysis showed that the mono-3d-metal di-gold(I) trinuclear heterobimetallic complexes were constructed through gold(I)-metal interactions. Metallophilic interactions were also investigated by quantum chemical calculations including the AIM and IGMH methods.

Real-time observation of the Woodward-Hoffmann rule for 1,3-cyclohexadiene by femtosecond soft X-ray transient absorption.

The stereochemistry of pericyclic reactions is explained by orbital symmetry conservation, referred to as the Woodward-Hoffmann (WH) rule. Although this rule has been verified using the structures of reactants and products, the temporal evolution of the orbital symmetry during the reaction has not been clarified. Herein, we used femtosecond soft X-ray transient absorption spectroscopy to elucidate the thermal pericyclic reaction of 1,3-cyclohexadiene (CHD) molecules, i.e., their isomerization to 1,3,5-hexatriene. In the present experimental scheme, the ring-opening reaction is driven by the thermal vibrational energy induced by photoexcitation to the Rydberg states at 6.2 eV and subsequent femtosecond relaxation to the ground state of CHD molecules. The direction of the ring opening, which can be conrotatory or disrotatory, was the primary focus, and the WH rule predicts the disrotatory pathway in the thermal process. We observed the shifts in K-edge absorption of the carbon atom from the 1s orbital to vacant molecular orbitals around 285 eV at a delay between 340 and 600 fs. Furthermore, a theoretical investigation predicts that the shifts depend on the molecular structures along the reaction pathways and the observed shifts in induced absorption are attributed to the structural change in the disrotatory pathway. This confirms that the orbital symmetry is dynamically conserved in the ring-opening reaction of CHD molecules as predicted using the WH rule.

Size dependent electrocatalytic activities of h-BN for oxygen reduction reaction to water.

Electrocatalytic activities for the oxygen reduction reaction (ORR) of Au electrodes modified by as prepared and size selected (0.45-1.0, 0.22-0.45, and 0.1-0.22 µm) h-BN nanosheet (BNNS), which is an insulator, were examined in O2 saturated 0.5M H2SO4 solution. The overpotential was reduced by all the BNNS modifications, and the smaller the size, the smaller the overpotential for ORR, i.e., the larger the ORR activity, in this size range. The overpotential was reduced by as much as ∼330 mV compared to a bare Au electrode by modifying the Au surface by the BNNS of the smallest size range (0.1-0.22 µm). The overpotential at this electrode was only 80 mV more than that at the Pt electrode. Both the rotation disk electrode experiments with Koutecky-Levich analysis and rotating ring disk electrode measurements showed that more than 80% of oxygen is reduced to water via the four-electron process at this electrode. These results strongly suggest and theoretical density functional theory calculations support that the ORR active sites are located at the edges of BNNS islands adsorbed on Au(111). The decrease in size of BNNS islands results in an effective increase in the number of the catalytically active sites and, hence, in the increase in the catalytic activity of the BNNS/Au(111) system for ORR.

Superior Multielectron-Transferring Energy Storage by π-d Conjugated Frameworks.

Reversible multielectron-transfer materials are of considerable interest because of the potential impact to advance present electrochemical energy storage technology by boosting energy density. To date, a few oxide-based materials can reach an electron-transfer number per metal-cation (eM ) larger than 2 upon a (de)intercalation mechanism. However, these materials suffer from degradation due to irreversible rearrangements of the cation-oxygen bonds, and are based on precious metals, for example, Ir and Ru. Hence, a design of the non-oxide-based reversible multielectron-transfer materials with abundant elements can provide a promising alternative. Herein, it is demonstrated that the bis(diimino)copper framework can show eM  = 3.5 with cation/anion co-redox mechanism together with a dual-ion mechanism. In this study, the role of the cation-anion interactions is unveiled by using an experiment/theory collaboration applied to a series of the model non-oxide abundant electrode systems based on different metal-nitrogen bonds. These models provide designer multielectron-transfer due to the tunable π-d conjugated electronic structures. It is found that the Cu-nitrogen bonds show a unique reversible rearrangement upon Li-intercalation, and this process responds to acquire a significant reversible multielectron-transfer. This work provides new insights into the affordable multielectron-transfer electrodes and uncovers an alternative strategy to advance the electrochemical energy storage reactions.

Ligand release from silicon phthalocyanine dyes triggered by X-ray irradiation.

Ligand release from silicon phthalocyanine (SiPc) dyes triggered by near-infrared (NIR) light is a key photochemical reaction involving caged compounds based on SiPc. Although NIR light is relatively permeable compared with visible light, this light can be attenuated by tissue absorption and scattering; therefore, using light to induce photochemical reactions deep inside the body is difficult. Herein, because X-rays are highly permeable and can produce radicals through the radiolysis of water, we investigated whether the axial ligands of SiPcs can be cleaved using X-ray irradiation. SiPcs with different axial ligands (alkoxy, siloxy, oxycarbonyl, and phenoxy groups) were irradiated with X-rays under hypoxic conditions. We found that the axial ligands were cleaved via reactions with hydrated electrons (e-aq), not OH radicals, generated from water in response to X-ray irradiation, and SiPc with alkoxy groups exhibited the highest cleavage efficiency. A quantitative investigation revealed that X-ray-induced axial ligand cleavage proceeds via a radical chain reaction. The reaction is expected to be applicable to the molecular design of X-ray-activatable functional molecules in the future.

Natural reaction orbitals for characterizing electron transfer responsive to nuclear coordinate displacement.

The natural reaction orbital (NRO) is proposed as a new concept for analyzing chemical reactions from the viewpoint of the electronic theory. The pair of the occupied and virtual NROs that characterize electron transfer responsive to nuclear coordinate displacement along the reaction path is automatically extracted from the solution of the coupled-perturbed self-consistent-field (CPSCF) equation for the perturbation of the nuclear displacement. The NRO-based reaction analysis method is applied to several reactions. As a result, it is found that the sum of squares of the singular values, derived from the solution of the CPSCF equation, gives sharp peaks around the transition state structures and at the shoulders of the potential energy curve. The peaks around the transition states suggest a new physical meaning of transition state from the viewpoint of the electronic theory. Furthermore, the double peaks reveal the asynchronous processes of reactions, which are not always shown in potential energy analyses. Since the NRO-based reaction analysis method is universal and robust for describing reaction mechanisms from an electronic theory viewpoint, it is expected to lead to universal reaction analyses based on the electronic theory.

Excited States of Metal-Adsorbed Dimethyl Disulfide: A TDDFT Study with Cluster Model.

The optical near field refers to a localized light field near a surface that can induce photochemical phenomena such as dipole-forbidden transitions. Recently, the photodissociation of the S-S bond of dimethyl disulfide (DMDS) was investigated using a scanning tunneling microscope with far- and near-field light. This reaction is thought to be initiated by the lowest-energy highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) transition of the DMDS molecule under far-field light. In near-field light, photodissociation proceeds at lower photon energies than in far-field light. To gain insight into the underlying mechanism, we theoretically investigated the excited states of DMDS adsorbed on Cu and Ag surfaces modeled by a tetrahedral 20-atom cluster. The frontier orbitals of the molecule were delocalized by the interaction with the metal, resulting in narrowing of the HOMO-LUMO gap energy. The excited-state distribution was analyzed using the Mulliken population analysis, decomposing molecular orbitals into metal and DMDS fragments. The excited states of the intra-DMDS transitions were found over a wider energy range, but at low energies, their oscillator strengths were negligible, which is consistent with the experimental results. Sparse modeling analysis showed that typical electronic transitions differed between the higher and lower excited states. If these low-lying excited states are efficiently excited by near-field light with different selection rules, the S-S bond dissociation reaction can proceed.

Extension of natural reaction orbital approach to multiconfigurational wavefunctions.

Recently, we proposed a new orbital analysis method, natural reaction orbital (NRO), which automatically extracts orbital pairs that characterize electron transfer in reaction processes by singular value decomposition of the first-order orbital response matrix to the nuclear coordinate displacements [Ebisawa et al., Phys. Chem. Chem. Phys. 24, 3532 (2022)]. NRO analysis along the intrinsic reaction coordinate (IRC) for several typical chemical reactions demonstrated that electron transfer occurs mainly in the vicinity of transition states and in regions where the energy profile along the IRC shows shoulder features, allowing the reaction mechanism to be explained in terms of electron motion. However, its application has been limited to single configuration theories such as Hartree-Fock theory and density functional theory. In this work, the concept of NRO is extended to multiconfigurational wavefunctions and formulated as the multiconfiguration NRO (MC-NRO). The MC-NRO method is applicable to various types of electronic structure theories, including multiconfigurational theory and linear response theory, and is expected to be a practical tool for extracting the essential qualitative features of a broad range of chemical reactions, including covalent bond dissociation and chemical reactions in electronically excited states. In this paper, we calculate the IRC for five basic chemical reaction processes at the level of the complete active space self-consistent field theory and discuss the phenomenon of electron transfer by performing MC-NRO analysis along each IRC. Finally, issues and future prospects of the MC-NRO method are discussed.

Doping-Mediated Energy-Level Engineering of M@Au12 Superatoms (M=Pd, Pt, Rh, Ir) for Efficient Photoluminescence and Photocatalysis.

We synthesized a series of MAu12 (dppe)5 Cl2 (MAu12 ; M=Au, Pd, Pt, Rh, or Ir; dppe=1,2-bis(diphenylphosphino)ethane), which have icosahedral M@Au12 superatomic cores, and systematically investigated their electronic structures, photoluminescence (PL) and photocatalytic properties. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) was expanded when doping an M element positioned at the lower left of the periodic table. The PL quantum yield was enhanced with an increase in the HOMO-LUMO gap and reached 0.46-0.67 for MAu12 (M=Pt, Rh, or Ir) under deaerated conditions. The bright PLs from MAu12 (M=Pt, Rh, or Ir) were assigned to phosphorescence based on quenching by O2 . MAu12 (M=Pt, Rh, or Ir) acted as a more efficient and stable photocatalyst than Au13 for intramolecular [2+2] cycloaddition of bisenone via the oxidative quenching cycle. This study provides rational guides for designing photoluminescent and photocatalytic gold superatoms by the doping of heterometal elements.

Photoluminescence of Doped Superatoms M@Au12 (M = Ru, Rh, Ir) Homoleptically Capped by (Ph2)PCH2P(Ph2): Efficient Room-Temperature Phosphorescence from Ru@Au12.

A series of doped gold superatoms M@Au12 (M = Ru, Rh, Ir) was synthesized by capping with the bidentate ligand (Ph2)PCH2P(Ph2). A single-crystal X-ray diffraction analysis showed that all the M@Au12 superatoms had icosahedral motifs with a significantly higher symmetry than that of the pure Au13 counterpart due to different coordination geometries. The Ru@Au12 superatom exhibited a room-temperature phosphorescence with the highest quantum yield of 0.37 in deaerated dichloromethane. Density functional theory calculations suggested that the efficient phosphorescence is ascribed to a rapid intersystem crossing due to the similarity between the singlet and triplet excited states in terms of structure and energy.